5.2 THE DER EXERCISES 5.2 21. Exercises 1-10. Calculate Ly (P) and Uf (P). x E [0, 21; P = {0, , , 1,2} . 2. f(x) = 1-x, 22. 23. 24. 11. Let f be a function continuous on [-1, 1] and take P as a partition of [-1,1]. Show that each of the following three statements is false. (a) L(P) = 3 and U(P) = 2. (b) Lr(P) = 3, U(P)=6, (c) Lf(P)-3, Ur(P) = 6, Ex and f(x)dz=2. no and f(x)ax=10. sw 12, (a) Given that P = {xo. ì§, ,xal is an arbitrary partition 25 of [a, b], find LXP) and UKP) for f(x) = x + 3. (b) Use your answers to part (a) to evaluate 27 f(x)dx. 29 13. Exercise 12 taking f(x)-3. 14, Exercise 12 taking f(x) = 1 + 2x. 5.3 THE FUNCTION E(
